Craiem Damian, Armentano Ricardo L
Favaloro Unversity, Facultad de Ingeniería, Ciencias Exactas y Naturales, Buenos Aires, Argentina.
Biorheology. 2007;44(4):251-63.
Arterial viscoelasticity can be described with a complex modulus (E*) in the frequency domain. In arteries, E* presents a power-law response with a plateau for higher frequencies. Constitutive models based on a combination of purely elastic and viscous elements can be represented with integer order differential equations but show several limitations. Recently, fractional derivative models with fewer parameters have proven to be efficient in describing rheological tissues. A new element, called "spring-pot", that interpolates between springs and dashpots is incorporated. Starting with a Voigt model, we proposed two fractional alternative models with one and two spring-pots. The three models were tested in an anesthetized sheep in a control state and during smooth muscle activation. A least squares method was used to fit E*. Local activation induced a vascular constriction with no pressure changes. The E* results confirmed the steep increase from static to dynamic values and a plateau in the range 2-30 Hz, coherent with fractional model predictions. Activation increased E*, affecting its real and imaginary parts separately. Only the model with two spring-pots correctly followed this behavior with the best performance in terms of least squares errors. In a context where activation separately modifies E*, this alternative model should be considered in describing arterial viscoelasticity in vivo.
动脉粘弹性可以在频域中用复模量（E*）来描述。在动脉中，E呈现幂律响应，在较高频率下有一个平台期。基于纯弹性和粘性元件组合的本构模型可以用整数阶微分方程表示，但存在一些局限性。最近，参数较少的分数阶导数模型已被证明在描述流变组织方面是有效的。引入了一种新的元件，称为“弹簧壶”，它在弹簧和阻尼器之间进行插值。从Voigt模型出发，我们提出了两个分别带有一个和两个弹簧壶的分数阶替代模型。这三个模型在麻醉绵羊处于对照状态和平滑肌激活期间进行了测试。使用最小二乘法拟合E。局部激活引起血管收缩但无压力变化。E的结果证实了从静态值到动态值的急剧增加以及在2 - 30 Hz范围内的平台期，这与分数阶模型预测一致。激活增加了E，分别影响其实部和虚部。只有带有两个弹簧壶的模型正确地遵循了这种行为，在最小二乘误差方面表现最佳。在激活分别改变E*的情况下，在描述体内动脉粘弹性时应考虑这种替代模型。
